分数阶扩散的三维液晶方程的整体正则性

数学物理学报 ›› 2020, Vol. 40 ›› Issue (4): 918-924.

分数阶扩散的三维液晶方程的整体正则性

李强()

^{河南理工大学数学与信息科学学院河南焦作 454000}

收稿日期:2019-06-20 出版日期:2020-08-26 发布日期:2020-08-20
作者简介:李强, E-mail:1220494943@qq.com

Global Regularity for the 3D Liquid Crystal Equations with Fractional Diffusion

Qiang Li()

^{School of Mathematics and Information Science, Henan Polytechnic University, Henan Jiaozuo 454000}

Received:2019-06-20 Online:2020-08-26 Published:2020-08-20

摘要/Abstract

摘要：

该文考虑的是带有分数阶耗散项 $(-\Delta)^{\alpha}u$ 和 $(-\Delta)^{\beta}d$ 的广义不可压缩液晶模型.目标是在需要最小的耗散情况下建立整体正则性.在初值充分光滑的情况下，若耗散指标 $\alpha\geq\frac{5}{4}$ , $\beta\geq\frac{5}{4}$ ,方程组有唯一的整体光滑解.

关键词: 液晶方程, 分数阶耗散, 整体正则性

Abstract:

In this paper, the focus is the global regularity of three-dimensional liquid crystal equations with fractional dissipations $(-\Delta)^{\alpha}u$ and $(-\Delta)^{\beta}d$ . The objective is to establish the global regularity of the fractional liquid crystal equations with the minimal amount of dissipations. And it is obtained that the equations have a global classical solution with sufficiently smooth data if $\alpha\geq\frac{5}{4}$ and $\beta\geq\frac{5}{4}$ .

Key words: Liquid crystal equations, Fractional dissipation, Global regularity

中图分类号:

O175.29

李强. 分数阶扩散的三维液晶方程的整体正则性[J]. 数学物理学报, 2020, 40(4): 918-924.

Qiang Li. Global Regularity for the 3D Liquid Crystal Equations with Fractional Diffusion[J]. Acta mathematica scientia,Series A, 2020, 40(4): 918-924.

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